The focus of this research project is two fold: one is the general treatment of learning control scheme and the other is the study of learning mechanism of neural networks viewed from the system theoretic viewpoint. Needless to say, these two issues are mutually related.In the study of the general learning control scheme, results on stability conditions in the frequency domain, robust stability condition under plant perturbations are obtained. these results guaranteed that robustness analysis can be made for such learning schemes as modified repetitive control schemes based upon the methodology already employed for finite-dimensional systems.In relation to these, it is also clarified that the learning mechanism of neural networks and its application to control systems can be unified into the principle that the association of unorganized memories and the optimization in their respective parameter space. The notion of composite networks to be described below is the key to this development.In the study of neural networks, the fundamental standpoint of viewing networks as dynamical systems led to the following subjects: 1) derivation of a learning algorithm for general networks with feedback connections, 2) its application to pattern recognition, 3) its further generalization to composite networks, 4) application of more effective algorithms such as the conjugate gradient method, each leading to a satisfactory result. In particular, the composite networks enjoy such features as 1) making learning easier by decomposing the problem into smaller parts, 2) applicable to networks where teaching signals are implicit, and are expected to become more fundamental to various construction of neural networks.On the other hand, it has also become clear that more theoretical analysis is fairly difficult, partly due to the fundamental nonlinearity. More detailed research in this direction can be an open problem for the future.